Finely grind the pistachios in a food processor until coarse.
In a medium saucepan, combine ground pistachios, sugar, cornstarch, and salt.
Slowly whisk in the milk until smooth.
Place the saucepan over medium heat and cook, stirring constantly.
Once thickened, reduce heat to low and add butter and vanilla.
Remove from heat and let cool slightly.
Pour into serving bowls and cover with plastic wrap.
Chill in the refrigerator for at least 2 hours.
Serve topped with whipped cream and chopped pistachios.